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⇱ man double_blas_level2 (3): double

double_blas_level2(3) double

Functions


subroutine dgbmv (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGBMV
subroutine dgemv (TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
subroutine dger (M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
DGER
subroutine dsbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DSBMV
subroutine dspmv (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
DSPMV
subroutine dspr (UPLO, N, ALPHA, X, INCX, AP)
DSPR
subroutine dspr2 (UPLO, N, ALPHA, X, INCX, Y, INCY, AP)
DSPR2
subroutine dsymv (UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DSYMV
subroutine dsyr (UPLO, N, ALPHA, X, INCX, A, LDA)
DSYR
subroutine dsyr2 (UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
DSYR2
subroutine dtbmv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
DTBMV
subroutine dtbsv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
DTBSV
subroutine dtpmv (UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV
subroutine dtpsv (UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPSV
subroutine dtrmv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
DTRMV

Detailed Description

This is the group of double LEVEL 2 BLAS routines.

Function Documentation

subroutine dgbmv (character TRANS, integer M, integer N, integer KL, integer KU, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(*) X, integer INCX, double precision BETA, double precision, dimension(*) Y, integer INCY)

DGBMV

Purpose: 

 DGBMV performs one of the matrix-vector operations
 y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y,
 where alpha and beta are scalars, x and y are vectors and A is an
 m by n band matrix, with kl sub-diagonals and ku super-diagonals.


 

Parameters:

TRANS 
 TRANS is CHARACTER*1
 On entry, TRANS specifies the operation to be performed as
 follows:
 TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
 TRANS = 'T' or 't' y := alpha*A**T*x + beta*y.
 TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y.


M 

 M is INTEGER
 On entry, M specifies the number of rows of the matrix A.
 M must be at least zero.


N 

 N is INTEGER
 On entry, N specifies the number of columns of the matrix A.
 N must be at least zero.


KL 

 KL is INTEGER
 On entry, KL specifies the number of sub-diagonals of the
 matrix A. KL must satisfy 0 .le. KL.


KU 

 KU is INTEGER
 On entry, KU specifies the number of super-diagonals of the
 matrix A. KU must satisfy 0 .le. KU.


ALPHA 

 ALPHA is DOUBLE PRECISION.
 On entry, ALPHA specifies the scalar alpha.


A 

 A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
 Before entry, the leading ( kl + ku + 1 ) by n part of the
 array A must contain the matrix of coefficients, supplied
 column by column, with the leading diagonal of the matrix in
 row ( ku + 1 ) of the array, the first super-diagonal
 starting at position 2 in row ku, the first sub-diagonal
 starting at position 1 in row ( ku + 2 ), and so on.
 Elements in the array A that do not correspond to elements
 in the band matrix (such as the top left ku by ku triangle)
 are not referenced.
 The following program segment will transfer a band matrix
 from conventional full matrix storage to band storage:
 DO 20, J = 1, N
 K = KU + 1 - J
 DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
 A( K + I, J ) = matrix( I, J )
 10 CONTINUE
 20 CONTINUE


LDA 

 LDA is INTEGER
 On entry, LDA specifies the first dimension of A as declared
 in the calling (sub) program. LDA must be at least
 ( kl + ku + 1 ).


X 

 X is DOUBLE PRECISION array of DIMENSION at least
 ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
 and at least
 ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
 Before entry, the incremented array X must contain the
 vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


BETA 

 BETA is DOUBLE PRECISION.
 On entry, BETA specifies the scalar beta. When BETA is
 supplied as zero then Y need not be set on input.


Y 

 Y is DOUBLE PRECISION array of DIMENSION at least
 ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
 and at least
 ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
 Before entry, the incremented array Y must contain the
 vector y. On exit, Y is overwritten by the updated vector y.


INCY 

 INCY is INTEGER
 On entry, INCY specifies the increment for the elements of
 Y. INCY must not be zero.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2015

Further Details: 

 Level 2 Blas routine.
 The vector and matrix arguments are not referenced when N = 0, or M = 0
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dgemv (character TRANS, integer M, integer N, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(*) X, integer INCX, double precision BETA, double precision, dimension(*) Y, integer INCY)

DGEMV

Purpose: 

 DGEMV performs one of the matrix-vector operations
 y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y,
 where alpha and beta are scalars, x and y are vectors and A is an
 m by n matrix.


 

Parameters:

TRANS 
 TRANS is CHARACTER*1
 On entry, TRANS specifies the operation to be performed as
 follows:
 TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
 TRANS = 'T' or 't' y := alpha*A**T*x + beta*y.
 TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y.


M 

 M is INTEGER
 On entry, M specifies the number of rows of the matrix A.
 M must be at least zero.


N 

 N is INTEGER
 On entry, N specifies the number of columns of the matrix A.
 N must be at least zero.


ALPHA 

 ALPHA is DOUBLE PRECISION.
 On entry, ALPHA specifies the scalar alpha.


A 

 A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
 Before entry, the leading m by n part of the array A must
 contain the matrix of coefficients.


LDA 

 LDA is INTEGER
 On entry, LDA specifies the first dimension of A as declared
 in the calling (sub) program. LDA must be at least
 max( 1, m ).


X 

 X is DOUBLE PRECISION array of DIMENSION at least
 ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
 and at least
 ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
 Before entry, the incremented array X must contain the
 vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


BETA 

 BETA is DOUBLE PRECISION.
 On entry, BETA specifies the scalar beta. When BETA is
 supplied as zero then Y need not be set on input.


Y 

 Y is DOUBLE PRECISION array of DIMENSION at least
 ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
 and at least
 ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
 Before entry with BETA non-zero, the incremented array Y
 must contain the vector y. On exit, Y is overwritten by the
 updated vector y.


INCY 

 INCY is INTEGER
 On entry, INCY specifies the increment for the elements of
 Y. INCY must not be zero.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2015

Further Details: 

 Level 2 Blas routine.
 The vector and matrix arguments are not referenced when N = 0, or M = 0
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dger (integer M, integer N, double precision ALPHA, double precision, dimension(*) X, integer INCX, double precision, dimension(*) Y, integer INCY, double precision, dimension(lda,*) A, integer LDA)

DGER

Purpose: 

 DGER performs the rank 1 operation
 A := alpha*x*y**T + A,
 where alpha is a scalar, x is an m element vector, y is an n element
 vector and A is an m by n matrix.


 

Parameters:

M 
 M is INTEGER
 On entry, M specifies the number of rows of the matrix A.
 M must be at least zero.


N 

 N is INTEGER
 On entry, N specifies the number of columns of the matrix A.
 N must be at least zero.


ALPHA 

 ALPHA is DOUBLE PRECISION.
 On entry, ALPHA specifies the scalar alpha.


X 

 X is DOUBLE PRECISION array of dimension at least
 ( 1 + ( m - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the m
 element vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


Y 

 Y is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCY ) ).
 Before entry, the incremented array Y must contain the n
 element vector y.


INCY 

 INCY is INTEGER
 On entry, INCY specifies the increment for the elements of
 Y. INCY must not be zero.


A 

 A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
 Before entry, the leading m by n part of the array A must
 contain the matrix of coefficients. On exit, A is
 overwritten by the updated matrix.


LDA 

 LDA is INTEGER
 On entry, LDA specifies the first dimension of A as declared
 in the calling (sub) program. LDA must be at least
 max( 1, m ).


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

 Level 2 Blas routine.
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dsbmv (character UPLO, integer N, integer K, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(*) X, integer INCX, double precision BETA, double precision, dimension(*) Y, integer INCY)

DSBMV

Purpose: 

 DSBMV performs the matrix-vector operation
 y := alpha*A*x + beta*y,
 where alpha and beta are scalars, x and y are n element vectors and
 A is an n by n symmetric band matrix, with k super-diagonals.


 

Parameters:

UPLO 
 UPLO is CHARACTER*1
 On entry, UPLO specifies whether the upper or lower
 triangular part of the band matrix A is being supplied as
 follows:
 UPLO = 'U' or 'u' The upper triangular part of A is
 being supplied.
 UPLO = 'L' or 'l' The lower triangular part of A is
 being supplied.


N 

 N is INTEGER
 On entry, N specifies the order of the matrix A.
 N must be at least zero.


K 

 K is INTEGER
 On entry, K specifies the number of super-diagonals of the
 matrix A. K must satisfy 0 .le. K.


ALPHA 

 ALPHA is DOUBLE PRECISION.
 On entry, ALPHA specifies the scalar alpha.


A 

 A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
 Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
 by n part of the array A must contain the upper triangular
 band part of the symmetric matrix, supplied column by
 column, with the leading diagonal of the matrix in row
 ( k + 1 ) of the array, the first super-diagonal starting at
 position 2 in row k, and so on. The top left k by k triangle
 of the array A is not referenced.
 The following program segment will transfer the upper
 triangular part of a symmetric band matrix from conventional
 full matrix storage to band storage:
 DO 20, J = 1, N
 M = K + 1 - J
 DO 10, I = MAX( 1, J - K ), J
 A( M + I, J ) = matrix( I, J )
 10 CONTINUE
 20 CONTINUE
 Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
 by n part of the array A must contain the lower triangular
 band part of the symmetric matrix, supplied column by
 column, with the leading diagonal of the matrix in row 1 of
 the array, the first sub-diagonal starting at position 1 in
 row 2, and so on. The bottom right k by k triangle of the
 array A is not referenced.
 The following program segment will transfer the lower
 triangular part of a symmetric band matrix from conventional
 full matrix storage to band storage:
 DO 20, J = 1, N
 M = 1 - J
 DO 10, I = J, MIN( N, J + K )
 A( M + I, J ) = matrix( I, J )
 10 CONTINUE
 20 CONTINUE


LDA 

 LDA is INTEGER
 On entry, LDA specifies the first dimension of A as declared
 in the calling (sub) program. LDA must be at least
 ( k + 1 ).


X 

 X is DOUBLE PRECISION array of DIMENSION at least
 ( 1 + ( n - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the
 vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


BETA 

 BETA is DOUBLE PRECISION.
 On entry, BETA specifies the scalar beta.


Y 

 Y is DOUBLE PRECISION array of DIMENSION at least
 ( 1 + ( n - 1 )*abs( INCY ) ).
 Before entry, the incremented array Y must contain the
 vector y. On exit, Y is overwritten by the updated vector y.


INCY 

 INCY is INTEGER
 On entry, INCY specifies the increment for the elements of
 Y. INCY must not be zero.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

 Level 2 Blas routine.
 The vector and matrix arguments are not referenced when N = 0, or M = 0
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dspmv (character UPLO, integer N, double precision ALPHA, double precision, dimension(*) AP, double precision, dimension(*) X, integer INCX, double precision BETA, double precision, dimension(*) Y, integer INCY)

DSPMV

Purpose: 

 DSPMV performs the matrix-vector operation
 y := alpha*A*x + beta*y,
 where alpha and beta are scalars, x and y are n element vectors and
 A is an n by n symmetric matrix, supplied in packed form.


 

Parameters:

UPLO 
 UPLO is CHARACTER*1
 On entry, UPLO specifies whether the upper or lower
 triangular part of the matrix A is supplied in the packed
 array AP as follows:
 UPLO = 'U' or 'u' The upper triangular part of A is
 supplied in AP.
 UPLO = 'L' or 'l' The lower triangular part of A is
 supplied in AP.


N 

 N is INTEGER
 On entry, N specifies the order of the matrix A.
 N must be at least zero.


ALPHA 

 ALPHA is DOUBLE PRECISION.
 On entry, ALPHA specifies the scalar alpha.


AP 

 AP is DOUBLE PRECISION array of DIMENSION at least
 ( ( n*( n + 1 ) )/2 ).
 Before entry with UPLO = 'U' or 'u', the array AP must
 contain the upper triangular part of the symmetric matrix
 packed sequentially, column by column, so that AP( 1 )
 contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
 and a( 2, 2 ) respectively, and so on.
 Before entry with UPLO = 'L' or 'l', the array AP must
 contain the lower triangular part of the symmetric matrix
 packed sequentially, column by column, so that AP( 1 )
 contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
 and a( 3, 1 ) respectively, and so on.


X 

 X is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the n
 element vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


BETA 

 BETA is DOUBLE PRECISION.
 On entry, BETA specifies the scalar beta. When BETA is
 supplied as zero then Y need not be set on input.


Y 

 Y is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCY ) ).
 Before entry, the incremented array Y must contain the n
 element vector y. On exit, Y is overwritten by the updated
 vector y.


INCY 

 INCY is INTEGER
 On entry, INCY specifies the increment for the elements of
 Y. INCY must not be zero.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

 Level 2 Blas routine.
 The vector and matrix arguments are not referenced when N = 0, or M = 0
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dspr (character UPLO, integer N, double precision ALPHA, double precision, dimension(*) X, integer INCX, double precision, dimension(*) AP)

DSPR

Purpose: 

 DSPR performs the symmetric rank 1 operation
 A := alpha*x*x**T + A,
 where alpha is a real scalar, x is an n element vector and A is an
 n by n symmetric matrix, supplied in packed form.


 

Parameters:

UPLO 
 UPLO is CHARACTER*1
 On entry, UPLO specifies whether the upper or lower
 triangular part of the matrix A is supplied in the packed
 array AP as follows:
 UPLO = 'U' or 'u' The upper triangular part of A is
 supplied in AP.
 UPLO = 'L' or 'l' The lower triangular part of A is
 supplied in AP.


N 

 N is INTEGER
 On entry, N specifies the order of the matrix A.
 N must be at least zero.


ALPHA 

 ALPHA is DOUBLE PRECISION.
 On entry, ALPHA specifies the scalar alpha.


X 

 X is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the n
 element vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


AP 

 AP is DOUBLE PRECISION array of DIMENSION at least
 ( ( n*( n + 1 ) )/2 ).
 Before entry with UPLO = 'U' or 'u', the array AP must
 contain the upper triangular part of the symmetric matrix
 packed sequentially, column by column, so that AP( 1 )
 contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
 and a( 2, 2 ) respectively, and so on. On exit, the array
 AP is overwritten by the upper triangular part of the
 updated matrix.
 Before entry with UPLO = 'L' or 'l', the array AP must
 contain the lower triangular part of the symmetric matrix
 packed sequentially, column by column, so that AP( 1 )
 contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
 and a( 3, 1 ) respectively, and so on. On exit, the array
 AP is overwritten by the lower triangular part of the
 updated matrix.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

 Level 2 Blas routine.
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dspr2 (character UPLO, integer N, double precision ALPHA, double precision, dimension(*) X, integer INCX, double precision, dimension(*) Y, integer INCY, double precision, dimension(*) AP)

DSPR2

Purpose: 

 DSPR2 performs the symmetric rank 2 operation
 A := alpha*x*y**T + alpha*y*x**T + A,
 where alpha is a scalar, x and y are n element vectors and A is an
 n by n symmetric matrix, supplied in packed form.


 

Parameters:

UPLO 
 UPLO is CHARACTER*1
 On entry, UPLO specifies whether the upper or lower
 triangular part of the matrix A is supplied in the packed
 array AP as follows:
 UPLO = 'U' or 'u' The upper triangular part of A is
 supplied in AP.
 UPLO = 'L' or 'l' The lower triangular part of A is
 supplied in AP.


N 

 N is INTEGER
 On entry, N specifies the order of the matrix A.
 N must be at least zero.


ALPHA 

 ALPHA is DOUBLE PRECISION.
 On entry, ALPHA specifies the scalar alpha.


X 

 X is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the n
 element vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


Y 

 Y is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCY ) ).
 Before entry, the incremented array Y must contain the n
 element vector y.


INCY 

 INCY is INTEGER
 On entry, INCY specifies the increment for the elements of
 Y. INCY must not be zero.


AP 

 AP is DOUBLE PRECISION array of DIMENSION at least
 ( ( n*( n + 1 ) )/2 ).
 Before entry with UPLO = 'U' or 'u', the array AP must
 contain the upper triangular part of the symmetric matrix
 packed sequentially, column by column, so that AP( 1 )
 contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
 and a( 2, 2 ) respectively, and so on. On exit, the array
 AP is overwritten by the upper triangular part of the
 updated matrix.
 Before entry with UPLO = 'L' or 'l', the array AP must
 contain the lower triangular part of the symmetric matrix
 packed sequentially, column by column, so that AP( 1 )
 contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
 and a( 3, 1 ) respectively, and so on. On exit, the array
 AP is overwritten by the lower triangular part of the
 updated matrix.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

 Level 2 Blas routine.
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dsymv (character UPLO, integer N, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(*) X, integer INCX, double precision BETA, double precision, dimension(*) Y, integer INCY)

DSYMV

Purpose: 

 DSYMV performs the matrix-vector operation
 y := alpha*A*x + beta*y,
 where alpha and beta are scalars, x and y are n element vectors and
 A is an n by n symmetric matrix.


 

Parameters:

UPLO 
 UPLO is CHARACTER*1
 On entry, UPLO specifies whether the upper or lower
 triangular part of the array A is to be referenced as
 follows:
 UPLO = 'U' or 'u' Only the upper triangular part of A
 is to be referenced.
 UPLO = 'L' or 'l' Only the lower triangular part of A
 is to be referenced.


N 

 N is INTEGER
 On entry, N specifies the order of the matrix A.
 N must be at least zero.


ALPHA 

 ALPHA is DOUBLE PRECISION.
 On entry, ALPHA specifies the scalar alpha.


A 

 A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
 Before entry with UPLO = 'U' or 'u', the leading n by n
 upper triangular part of the array A must contain the upper
 triangular part of the symmetric matrix and the strictly
 lower triangular part of A is not referenced.
 Before entry with UPLO = 'L' or 'l', the leading n by n
 lower triangular part of the array A must contain the lower
 triangular part of the symmetric matrix and the strictly
 upper triangular part of A is not referenced.


LDA 

 LDA is INTEGER
 On entry, LDA specifies the first dimension of A as declared
 in the calling (sub) program. LDA must be at least
 max( 1, n ).


X 

 X is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the n
 element vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


BETA 

 BETA is DOUBLE PRECISION.
 On entry, BETA specifies the scalar beta. When BETA is
 supplied as zero then Y need not be set on input.


Y 

 Y is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCY ) ).
 Before entry, the incremented array Y must contain the n
 element vector y. On exit, Y is overwritten by the updated
 vector y.


INCY 

 INCY is INTEGER
 On entry, INCY specifies the increment for the elements of
 Y. INCY must not be zero.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

 Level 2 Blas routine.
 The vector and matrix arguments are not referenced when N = 0, or M = 0
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dsyr (character UPLO, integer N, double precision ALPHA, double precision, dimension(*) X, integer INCX, double precision, dimension(lda,*) A, integer LDA)

DSYR

Purpose: 

 DSYR performs the symmetric rank 1 operation
 A := alpha*x*x**T + A,
 where alpha is a real scalar, x is an n element vector and A is an
 n by n symmetric matrix.


 

Parameters:

UPLO 
 UPLO is CHARACTER*1
 On entry, UPLO specifies whether the upper or lower
 triangular part of the array A is to be referenced as
 follows:
 UPLO = 'U' or 'u' Only the upper triangular part of A
 is to be referenced.
 UPLO = 'L' or 'l' Only the lower triangular part of A
 is to be referenced.


N 

 N is INTEGER
 On entry, N specifies the order of the matrix A.
 N must be at least zero.


ALPHA 

 ALPHA is DOUBLE PRECISION.
 On entry, ALPHA specifies the scalar alpha.


X 

 X is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the n
 element vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


A 

 A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
 Before entry with UPLO = 'U' or 'u', the leading n by n
 upper triangular part of the array A must contain the upper
 triangular part of the symmetric matrix and the strictly
 lower triangular part of A is not referenced. On exit, the
 upper triangular part of the array A is overwritten by the
 upper triangular part of the updated matrix.
 Before entry with UPLO = 'L' or 'l', the leading n by n
 lower triangular part of the array A must contain the lower
 triangular part of the symmetric matrix and the strictly
 upper triangular part of A is not referenced. On exit, the
 lower triangular part of the array A is overwritten by the
 lower triangular part of the updated matrix.


LDA 

 LDA is INTEGER
 On entry, LDA specifies the first dimension of A as declared
 in the calling (sub) program. LDA must be at least
 max( 1, n ).


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

 Level 2 Blas routine.
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dsyr2 (character UPLO, integer N, double precision ALPHA, double precision, dimension(*) X, integer INCX, double precision, dimension(*) Y, integer INCY, double precision, dimension(lda,*) A, integer LDA)

DSYR2

Purpose: 

 DSYR2 performs the symmetric rank 2 operation
 A := alpha*x*y**T + alpha*y*x**T + A,
 where alpha is a scalar, x and y are n element vectors and A is an n
 by n symmetric matrix.


 

Parameters:

UPLO 
 UPLO is CHARACTER*1
 On entry, UPLO specifies whether the upper or lower
 triangular part of the array A is to be referenced as
 follows:
 UPLO = 'U' or 'u' Only the upper triangular part of A
 is to be referenced.
 UPLO = 'L' or 'l' Only the lower triangular part of A
 is to be referenced.


N 

 N is INTEGER
 On entry, N specifies the order of the matrix A.
 N must be at least zero.


ALPHA 

 ALPHA is DOUBLE PRECISION.
 On entry, ALPHA specifies the scalar alpha.


X 

 X is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the n
 element vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


Y 

 Y is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCY ) ).
 Before entry, the incremented array Y must contain the n
 element vector y.


INCY 

 INCY is INTEGER
 On entry, INCY specifies the increment for the elements of
 Y. INCY must not be zero.


A 

 A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
 Before entry with UPLO = 'U' or 'u', the leading n by n
 upper triangular part of the array A must contain the upper
 triangular part of the symmetric matrix and the strictly
 lower triangular part of A is not referenced. On exit, the
 upper triangular part of the array A is overwritten by the
 upper triangular part of the updated matrix.
 Before entry with UPLO = 'L' or 'l', the leading n by n
 lower triangular part of the array A must contain the lower
 triangular part of the symmetric matrix and the strictly
 upper triangular part of A is not referenced. On exit, the
 lower triangular part of the array A is overwritten by the
 lower triangular part of the updated matrix.


LDA 

 LDA is INTEGER
 On entry, LDA specifies the first dimension of A as declared
 in the calling (sub) program. LDA must be at least
 max( 1, n ).


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

 Level 2 Blas routine.
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dtbmv (character UPLO, character TRANS, character DIAG, integer N, integer K, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(*) X, integer INCX)

DTBMV

Purpose: 

 DTBMV performs one of the matrix-vector operations
 x := A*x, or x := A**T*x,
 where x is an n element vector and A is an n by n unit, or non-unit,
 upper or lower triangular band matrix, with ( k + 1 ) diagonals.


 

Parameters:

UPLO 
 UPLO is CHARACTER*1
 On entry, UPLO specifies whether the matrix is an upper or
 lower triangular matrix as follows:
 UPLO = 'U' or 'u' A is an upper triangular matrix.
 UPLO = 'L' or 'l' A is a lower triangular matrix.


TRANS 

 TRANS is CHARACTER*1
 On entry, TRANS specifies the operation to be performed as
 follows:
 TRANS = 'N' or 'n' x := A*x.
 TRANS = 'T' or 't' x := A**T*x.
 TRANS = 'C' or 'c' x := A**T*x.


DIAG 

 DIAG is CHARACTER*1
 On entry, DIAG specifies whether or not A is unit
 triangular as follows:
 DIAG = 'U' or 'u' A is assumed to be unit triangular.
 DIAG = 'N' or 'n' A is not assumed to be unit
 triangular.


N 

 N is INTEGER
 On entry, N specifies the order of the matrix A.
 N must be at least zero.


K 

 K is INTEGER
 On entry with UPLO = 'U' or 'u', K specifies the number of
 super-diagonals of the matrix A.
 On entry with UPLO = 'L' or 'l', K specifies the number of
 sub-diagonals of the matrix A.
 K must satisfy 0 .le. K.


A 

 A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
 Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
 by n part of the array A must contain the upper triangular
 band part of the matrix of coefficients, supplied column by
 column, with the leading diagonal of the matrix in row
 ( k + 1 ) of the array, the first super-diagonal starting at
 position 2 in row k, and so on. The top left k by k triangle
 of the array A is not referenced.
 The following program segment will transfer an upper
 triangular band matrix from conventional full matrix storage
 to band storage:
 DO 20, J = 1, N
 M = K + 1 - J
 DO 10, I = MAX( 1, J - K ), J
 A( M + I, J ) = matrix( I, J )
 10 CONTINUE
 20 CONTINUE
 Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
 by n part of the array A must contain the lower triangular
 band part of the matrix of coefficients, supplied column by
 column, with the leading diagonal of the matrix in row 1 of
 the array, the first sub-diagonal starting at position 1 in
 row 2, and so on. The bottom right k by k triangle of the
 array A is not referenced.
 The following program segment will transfer a lower
 triangular band matrix from conventional full matrix storage
 to band storage:
 DO 20, J = 1, N
 M = 1 - J
 DO 10, I = J, MIN( N, J + K )
 A( M + I, J ) = matrix( I, J )
 10 CONTINUE
 20 CONTINUE
 Note that when DIAG = 'U' or 'u' the elements of the array A
 corresponding to the diagonal elements of the matrix are not
 referenced, but are assumed to be unity.


LDA 

 LDA is INTEGER
 On entry, LDA specifies the first dimension of A as declared
 in the calling (sub) program. LDA must be at least
 ( k + 1 ).


X 

 X is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the n
 element vector x. On exit, X is overwritten with the
 transformed vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

 Level 2 Blas routine.
 The vector and matrix arguments are not referenced when N = 0, or M = 0
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dtbsv (character UPLO, character TRANS, character DIAG, integer N, integer K, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(*) X, integer INCX)

DTBSV

Purpose: 

 DTBSV solves one of the systems of equations
 A*x = b, or A**T*x = b,
 where b and x are n element vectors and A is an n by n unit, or
 non-unit, upper or lower triangular band matrix, with ( k + 1 )
 diagonals.
 No test for singularity or near-singularity is included in this
 routine. Such tests must be performed before calling this routine.


 

Parameters:

UPLO 
 UPLO is CHARACTER*1
 On entry, UPLO specifies whether the matrix is an upper or
 lower triangular matrix as follows:
 UPLO = 'U' or 'u' A is an upper triangular matrix.
 UPLO = 'L' or 'l' A is a lower triangular matrix.


TRANS 

 TRANS is CHARACTER*1
 On entry, TRANS specifies the equations to be solved as
 follows:
 TRANS = 'N' or 'n' A*x = b.
 TRANS = 'T' or 't' A**T*x = b.
 TRANS = 'C' or 'c' A**T*x = b.


DIAG 

 DIAG is CHARACTER*1
 On entry, DIAG specifies whether or not A is unit
 triangular as follows:
 DIAG = 'U' or 'u' A is assumed to be unit triangular.
 DIAG = 'N' or 'n' A is not assumed to be unit
 triangular.


N 

 N is INTEGER
 On entry, N specifies the order of the matrix A.
 N must be at least zero.


K 

 K is INTEGER
 On entry with UPLO = 'U' or 'u', K specifies the number of
 super-diagonals of the matrix A.
 On entry with UPLO = 'L' or 'l', K specifies the number of
 sub-diagonals of the matrix A.
 K must satisfy 0 .le. K.


A 

 A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
 Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
 by n part of the array A must contain the upper triangular
 band part of the matrix of coefficients, supplied column by
 column, with the leading diagonal of the matrix in row
 ( k + 1 ) of the array, the first super-diagonal starting at
 position 2 in row k, and so on. The top left k by k triangle
 of the array A is not referenced.
 The following program segment will transfer an upper
 triangular band matrix from conventional full matrix storage
 to band storage:
 DO 20, J = 1, N
 M = K + 1 - J
 DO 10, I = MAX( 1, J - K ), J
 A( M + I, J ) = matrix( I, J )
 10 CONTINUE
 20 CONTINUE
 Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
 by n part of the array A must contain the lower triangular
 band part of the matrix of coefficients, supplied column by
 column, with the leading diagonal of the matrix in row 1 of
 the array, the first sub-diagonal starting at position 1 in
 row 2, and so on. The bottom right k by k triangle of the
 array A is not referenced.
 The following program segment will transfer a lower
 triangular band matrix from conventional full matrix storage
 to band storage:
 DO 20, J = 1, N
 M = 1 - J
 DO 10, I = J, MIN( N, J + K )
 A( M + I, J ) = matrix( I, J )
 10 CONTINUE
 20 CONTINUE
 Note that when DIAG = 'U' or 'u' the elements of the array A
 corresponding to the diagonal elements of the matrix are not
 referenced, but are assumed to be unity.


LDA 

 LDA is INTEGER
 On entry, LDA specifies the first dimension of A as declared
 in the calling (sub) program. LDA must be at least
 ( k + 1 ).


X 

 X is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the n
 element right-hand side vector b. On exit, X is overwritten
 with the solution vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

 Level 2 Blas routine.
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dtpmv (character UPLO, character TRANS, character DIAG, integer N, double precision, dimension(*) AP, double precision, dimension(*) X, integer INCX)

DTPMV

Purpose: 

 DTPMV performs one of the matrix-vector operations
 x := A*x, or x := A**T*x,
 where x is an n element vector and A is an n by n unit, or non-unit,
 upper or lower triangular matrix, supplied in packed form.


 

Parameters:

UPLO 
 UPLO is CHARACTER*1
 On entry, UPLO specifies whether the matrix is an upper or
 lower triangular matrix as follows:
 UPLO = 'U' or 'u' A is an upper triangular matrix.
 UPLO = 'L' or 'l' A is a lower triangular matrix.


TRANS 

 TRANS is CHARACTER*1
 On entry, TRANS specifies the operation to be performed as
 follows:
 TRANS = 'N' or 'n' x := A*x.
 TRANS = 'T' or 't' x := A**T*x.
 TRANS = 'C' or 'c' x := A**T*x.


DIAG 

 DIAG is CHARACTER*1
 On entry, DIAG specifies whether or not A is unit
 triangular as follows:
 DIAG = 'U' or 'u' A is assumed to be unit triangular.
 DIAG = 'N' or 'n' A is not assumed to be unit
 triangular.


N 

 N is INTEGER
 On entry, N specifies the order of the matrix A.
 N must be at least zero.


AP 

 AP is DOUBLE PRECISION array of DIMENSION at least
 ( ( n*( n + 1 ) )/2 ).
 Before entry with UPLO = 'U' or 'u', the array AP must
 contain the upper triangular matrix packed sequentially,
 column by column, so that AP( 1 ) contains a( 1, 1 ),
 AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
 respectively, and so on.
 Before entry with UPLO = 'L' or 'l', the array AP must
 contain the lower triangular matrix packed sequentially,
 column by column, so that AP( 1 ) contains a( 1, 1 ),
 AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
 respectively, and so on.
 Note that when DIAG = 'U' or 'u', the diagonal elements of
 A are not referenced, but are assumed to be unity.


X 

 X is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the n
 element vector x. On exit, X is overwritten with the
 transformed vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

 Level 2 Blas routine.
 The vector and matrix arguments are not referenced when N = 0, or M = 0
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dtpsv (character UPLO, character TRANS, character DIAG, integer N, double precision, dimension(*) AP, double precision, dimension(*) X, integer INCX)

DTPSV

Purpose: 

 DTPSV solves one of the systems of equations
 A*x = b, or A**T*x = b,
 where b and x are n element vectors and A is an n by n unit, or
 non-unit, upper or lower triangular matrix, supplied in packed form.
 No test for singularity or near-singularity is included in this
 routine. Such tests must be performed before calling this routine.


 

Parameters:

UPLO 
 UPLO is CHARACTER*1
 On entry, UPLO specifies whether the matrix is an upper or
 lower triangular matrix as follows:
 UPLO = 'U' or 'u' A is an upper triangular matrix.
 UPLO = 'L' or 'l' A is a lower triangular matrix.


TRANS 

 TRANS is CHARACTER*1
 On entry, TRANS specifies the equations to be solved as
 follows:
 TRANS = 'N' or 'n' A*x = b.
 TRANS = 'T' or 't' A**T*x = b.
 TRANS = 'C' or 'c' A**T*x = b.


DIAG 

 DIAG is CHARACTER*1
 On entry, DIAG specifies whether or not A is unit
 triangular as follows:
 DIAG = 'U' or 'u' A is assumed to be unit triangular.
 DIAG = 'N' or 'n' A is not assumed to be unit
 triangular.


N 

 N is INTEGER
 On entry, N specifies the order of the matrix A.
 N must be at least zero.


AP 

 AP is DOUBLE PRECISION array of DIMENSION at least
 ( ( n*( n + 1 ) )/2 ).
 Before entry with UPLO = 'U' or 'u', the array AP must
 contain the upper triangular matrix packed sequentially,
 column by column, so that AP( 1 ) contains a( 1, 1 ),
 AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
 respectively, and so on.
 Before entry with UPLO = 'L' or 'l', the array AP must
 contain the lower triangular matrix packed sequentially,
 column by column, so that AP( 1 ) contains a( 1, 1 ),
 AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
 respectively, and so on.
 Note that when DIAG = 'U' or 'u', the diagonal elements of
 A are not referenced, but are assumed to be unity.


X 

 X is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the n
 element right-hand side vector b. On exit, X is overwritten
 with the solution vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

 Level 2 Blas routine.
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

subroutine dtrmv (character UPLO, character TRANS, character DIAG, integer N, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(*) X, integer INCX)

DTRMV

Purpose: 

 DTRMV performs one of the matrix-vector operations
 x := A*x, or x := A**T*x,
 where x is an n element vector and A is an n by n unit, or non-unit,
 upper or lower triangular matrix.


 

Parameters:

UPLO 
 UPLO is CHARACTER*1
 On entry, UPLO specifies whether the matrix is an upper or
 lower triangular matrix as follows:
 UPLO = 'U' or 'u' A is an upper triangular matrix.
 UPLO = 'L' or 'l' A is a lower triangular matrix.


TRANS 

 TRANS is CHARACTER*1
 On entry, TRANS specifies the operation to be performed as
 follows:
 TRANS = 'N' or 'n' x := A*x.
 TRANS = 'T' or 't' x := A**T*x.
 TRANS = 'C' or 'c' x := A**T*x.


DIAG 

 DIAG is CHARACTER*1
 On entry, DIAG specifies whether or not A is unit
 triangular as follows:
 DIAG = 'U' or 'u' A is assumed to be unit triangular.
 DIAG = 'N' or 'n' A is not assumed to be unit
 triangular.


N 

 N is INTEGER
 On entry, N specifies the order of the matrix A.
 N must be at least zero.


A 

 A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
 Before entry with UPLO = 'U' or 'u', the leading n by n
 upper triangular part of the array A must contain the upper
 triangular matrix and the strictly lower triangular part of
 A is not referenced.
 Before entry with UPLO = 'L' or 'l', the leading n by n
 lower triangular part of the array A must contain the lower
 triangular matrix and the strictly upper triangular part of
 A is not referenced.
 Note that when DIAG = 'U' or 'u', the diagonal elements of
 A are not referenced either, but are assumed to be unity.


LDA 

 LDA is INTEGER
 On entry, LDA specifies the first dimension of A as declared
 in the calling (sub) program. LDA must be at least
 max( 1, n ).


X 

 X is DOUBLE PRECISION array of dimension at least
 ( 1 + ( n - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the n
 element vector x. On exit, X is overwritten with the
 transformed vector x.


INCX 

 INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

 Level 2 Blas routine.
 The vector and matrix arguments are not referenced when N = 0, or M = 0
 -- Written on 22-October-1986.
 Jack Dongarra, Argonne National Lab.
 Jeremy Du Croz, Nag Central Office.
 Sven Hammarling, Nag Central Office.
 Richard Hanson, Sandia National Labs.


 

Author

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